refactor(chat): reuse fullscreen back button

src/app/_components/__tests__/tailwind-components.test.tsx

@@ -21,6 +21,13 @@ describe("shared Tailwind components", () => {
         analyticsKey="chat.back_to_home"
       />,
     );
+    const unstyledHtml = renderToStaticMarkup(
+      <BackButton
+        onClick={() => undefined}
+        variant="unstyled"
+        className="custom-back"
+      />,
+    );
 
     expect(linkHtml).toContain('href="/chat"');
     expect(linkHtml).toContain('aria-label="Back to chat"');
@@ -35,6 +42,8 @@ describe("shared Tailwind components", () => {
     expect(darkHtml).toContain('data-analytics-key="chat.back_to_home"');
     expect(darkHtml).toContain("bg-[rgba(13,11,20,0.7)]");
     expect(darkHtml).toContain("text-white");
+    expect(unstyledHtml).toContain("custom-back");
+    expect(unstyledHtml).not.toContain("size-8");
   });
 
   it("renders CharacterAvatar with dynamic sizing and image utilities", () => {